Computing and Visualization in Science

, Volume 15, Issue 2, pp 75–86 | Cite as

Tensor structured evaluation of singular volume integrals

  • Jonas Ballani
  • Peter Meszmer


In this article, we introduce a new method for the accurate and fast computation of singular integrals over cuboids in three-dimensional space. Using a straightforward geometric parametrisation of the domain of integration, we interpret the integral as a smooth function on a high-dimensional parameter space. A standard interpolation scheme then leads to a high-dimensional tensor to which an approximation in the data-sparse hierarchical tensor format is applied. Once this approximation is available, the evaluation of an integral value becomes an easy task which does no longer require the treatment of singular terms. Numerical experiments illustrate the potential of the proposed approach for typical examples.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany

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